Comparison of frequency domain and time domain methods for the numerical simulation of contactless ultrasonic cavitation

The use of a top-mounted electromagnetic induction coil has been demonstrated as a contactless alternative to traditional ultrasonic treatment (UST) techniques that use an immersed mechanical sonotrode for the treatment of metals in the liquid state. This method offers similar benefits to existing UST approaches, including degassing, grain refinement, and dispersion of nanoparticles, while also preventing contact contamination due to erosion of the sonotrode. Contactless treatment potentially extends UST to high temperature or reactive melts. Generally, the method relies on acoustic resonance to reach pressure levels suitable for inertial cavitation and as a result the active cavitation volume tends to lie deep in the melt rather than in the small volume surrounding the immersed sonotrode probe. Consequently, (i) with suitable tuning of the coil supply frequency for resonance, the treatment volume can be made arbitrarily large, (ii) the problem of shielding and pressure wave attenuation suffered by the immersed sonotrode is avoided. However, relying on acoustic resonance presents problems: (i) the emergence of bubbles alters the speed of sound, resonance is momentarily lost, and cavitation becomes intermittent, (ii) as sound waves travel through and reflect on all the materials surrounding the melt, the sound characteristics of the crucible and supporting structures need to be carefully considered. The physics of cavitation coupled with this intermittent behaviour poses a challenge to sonotrode modelling orthodoxy, a problem we are trying to address in this publication. Two alternative approaches will be discussed, one of which is in the time domain and one in the frequency domain, which couple the solution of a bubble dynamics solver with that of an acoustics solver, to give an accurate prediction of the acoustic pressure generated by the induction coil. The time domain solver uses a novel algorithm to improve simulation time, by detecting an imminent bubble collapse and prescribing its subsequent behaviour, rather than directly solving a region that would normally require extremely small time steps. This way, it is shown to predict intermittent cavitation. The frequency domain solver for the first time couples the nonlinear Helmholtz model used for studying cavitation, with a background source term for the contribution of Lorentz forces. It predicts comparable RMS pressures to the time domain solver, but not the intermittent behaviour due to the underlying harmonic assumption. As further validation, the frequency domain method is also used to compare the generated acoustic pressure with that of traditional UST using a mechanical sonotrode.     

超声管形振子的振动分析

基于Flügge壳体理论,利用严格解法得出了自由边界条件下超声管形振子纵径耦合振动的频率方程,研究了长径比、径厚比及泊松比等参数对振子振动频率的影响,并和薄膜简支边界条件下的振动情况进行了对比;通过与表观弹性法进行比较研究,探讨了表观弹性法的精度;最后用严格解法计算了管形振子的振型曲线,对其纵径转换效率进行了分析。研究表明:在自由和薄膜简支两种边界条件下,随着长径比的增大,两种边界条件对管形振子纵径耦合振动无量纲频率影响的差异性减弱,且径厚比越大其差异性越小;在自由边界条件下,对于径厚比a/h>10的薄壳振子,径厚比的变化对无量纲频率的影响很小;在长径比一定时无量纲频率随泊松比的增大而减小,且泊松比对其的影响程度随长径比的变化而不同,当长径比l/a=π时影响最大;通过比较研究,证明三维表观弹性法具有很高的计算精度。     

Vibration analysis of ultrasonic tubular resonators

The frequency equation of the axisymmetric coupled vibration of a ultrasonic tubular resonator with both ends free is derived by an exact solution method,based on classical Fl(u|¨)gge thin shell theory.The dependence of the dinieiisionless frequencyΩon the ratio of length to radius l/a.the ratio of radius to thickness a/h and Poisson’s ratio v is investigated, and the axisymmetric coupled vibration of the ultrasonic tubular resonator with both ends shear diaphragm is compared with that with both ends free.The accuracy of two-dimensional and three-dimensional apparent elasticity method is also assessed by the comparison with the exact solution method.Finally,the mode shapes of the ultrasonic tubular resonator are calculated by the exact solution method,and its transform efficient is analyzed.The results show that as for two boundary conditions of both ends free and both ends shear diaphragm,the difference of the effect of the boundary conditions on the dinieiisionless frequency of the axisymmetric coupled vibration of the ultrasonic tubular resonator becomes smaller as l/a increases,and the larger a/h.the smaller the difference.Moreover,for free-free boundary conditions,the change of a/h has nearly no effect on the dinieiisionless frequency of the thin tubular resonator usually considered to mean a/h > 10.Furthermore,the dinieiisionless frequency fi decreases as v increases for a given l/a.and the impact of v onΩis different for different l/a.and the maximum impact will appear when l/a =π.Finally,the study also shows the three-dimensional apparent elasticity method has very high accuracy.     

Analysis of optical time domain demultiplexer using microring resonators

A time domain optical demultiplexer using electrooptic microring resonator is proposed. The switching window with pico-second order width is generated by using a sinusoidal electrical control voltage to shift the refractive index of the material. The modulation characteristics and switching window of the microring resonator are studied. The dependences of the width and extinction ratio of the switching window on the control voltage are analyzed. The demultiplexing performance of a 40–10 Gbps system is evaluated by numerical simulation technology. Results show that switching windows with required width and extinction ratio can be generated.     

Backscattering in silicon microring resonators: a quantitative analysis

Silicon microring resonators very often exhibit resonance splitting due to backscattering. This effect is hard to quantitatively and predicatively model. This paper presents a behavioral circuit model for microrings that quantitatively explains the wide variations in resonance splitting observed in experiments. The model is based on an in‐depth analysis of the contributions to backscattering by both the waveguides and couplers. Backscattering transforms unidirectional microrings into bidirectional circuits by coupling the clockwise and counterclockwise circulating modes. In high‐Q microrings, visible resonance splitting will be induced, but, due to the stochastic nature of backscattering, this splitting is different for each resonance. Our model, based on temporal coupled mode theory, and the associated fitting method, are both accurate and robust, and can also explain asymmetrically split resonances. The cause of asymmetric resonance splitting is identified as the backcoupling in the couplers. This is experimentally confirmed and its dependency on gap and coupling length is further analyzed. Moreover, the wide variation in resonance splitting of one spectrum is analyzed and successfully explained by our circuit model that incorporates most linear parasitic effects in the microring. This analysis uncovers multi‐cavity interference within the microring as an important source of this variation.

     

Nonlinear time series analysis of electrocardiograms

In recent years there has been an increasing number of papers in the literature, applying the methods and techniques of Nonlinear Dynamics to the time series of electrical activity in normal electrocardiograms (ECGs) of various human subjects. Most of these studies are based primarily on correlation dimension estimates, and conclude that the dynamics of the ECG signal is deterministic and occurs on a chaotic attractor, whose dimension can distinguish between healthy and severely malfunctioning cases. In this paper, we first demonstrate that correlation dimension calculations must be used with care, as they do not always yield reliable estimates of the attractor's "dimension." We then carry out a number of additional tests (time differencing, smoothing, principal component analysis, surrogate data analysis, etc.) on the ECGs of three "normal" subjects and three "heavy smokers" at rest and after mild exercising, whose cardiac rhythms look very similar. Our main conclusion is that no major dynamical differences are evident in these signals. A preliminary estimate of three to four basic variables governing the dynamics (based on correlation dimension calculations) is updated to five to six, when temporal correlations between points are removed. Finally, in almost all cases, the transition between resting and mild exercising seems to imply a small increase in the complexity of cardiac dynamics. (c) 1995 American Institute of Physics.     

超声空化去毛刺的理论分析及数值仿真

随着制造业的不断发展,对产品的加工精度要求愈来愈高,然而微小毛刺的去除仍然是十分困难的。毛刺虽小但危害巨大。因此,有效去除毛刺已成为加工中不可或缺的工序。而超声波去毛刺法可以有效快速的去除复杂零件的微小毛刺,具有很高的实用价值。尽管超声波的相关理论日趋完善,但是超声去毛刺机理以及空化产生的高压对毛刺的影响缺乏一些理论参考。此文阐述了超声波去毛刺的基本原理,利用有限元软件ABAQUS对单个空化泡在毛刺上的溃灭过程进行数值仿真,证明了超声波去毛刺的可行性,通过实验验证,超声波能够有效的去除毛刺。其研究结果为进一步研究超声波去毛刺的理论提供了参考。     

Quantitative MRS: comparison of time domain and time domain frequency domain methods using a novel test procedure

For quantitative analysis of in vivo MR spectra, a state-of-the-art time domain method was compared with a recently reported time domain frequency domain method which uses wavelets for background characterization. The comparison was made on the basis of results for simulated test problems that were constructed by combining measured and simulated MRS data at different signal-to-noise ratios in order to simultaneously reflect real world difficulties, in particular the overlapping background problem, and to allow for quantitative judgment of a method's accuracy. Incorporating prior knowledge was also considered. The results obtained give insight into the accuracy of the methods when applied to measured MRS data. Due to the improved background characterization, the time domain frequency domain method outperformed the time domain method in some of the test cases. Both methods were also applied to serial brain MR spectra of a healthy volunteer on 10 occasions.     

Nonlinear standing waves in 2-D acoustic resonators

This paper deals with 2-D simulation of finite-amplitude standing waves behavior in rectangular acoustic resonators. Set of three partial differential equations in third approximation formulated in conservative form is derived from fundamental equations of gas dynamics. These equations form a closed set for two components of acoustic velocity vector and density, the equations account for external driving force, gas dynamic nonlinearities and thermoviscous dissipation. Pressure is obtained from solution of the set by means of an analytical formula. The equations are formulated in the Cartesian coordinate system. The model equations set is solved numerically in time domain using a central semi-discrete difference scheme developed for integration of sets of convection-diffusion equations with two or more spatial coordinates. Numerical results show various patterns of acoustic field in resonators driven using vibrating piston with spatial distribution of velocity. Excitation of lateral shock-wave mode is observed when resonant conditions are fulfilled for longitudinal as well as for transversal direction along the resonator cavity.     

Parallel numerical simulation of the ultrasonic waves in a prestressed formation

Formation stress prediction plays an important role in petroleum production. Understanding ultrasonic wave propagation in a stress-induced anisotropic formation will help us to find an efficient method to correctly predict formation stress or formation pore pressure. In this work, a parallel 3D finite-difference time domain (FDTD) method is developed to simulate elastic wave propagation in pre-stressed formations. A perfectly matched layer (PML) is used as an absorbing boundary condition. The acceleration ration of total CPU computation time and the lasting time of the program run in the super computer-ShenTeng 6800 in the Super Computation Center of Chinese Academy of Science (CAS) are tested. It shows that the acceleration factor of the parallel FDTD program is considerably high even if the domain is only divided in one direction. When the total computation model size fixed, the acceleration factor of 8 CPU and 64 CPU is 3.0 and 13.8, respectively. The velocities under various static stresses are obtained by processing the array data calculated with the FDTD using Prony's method. The linear relation between velocity and the applied pre-stress is in agreement with that predicted by the acoustoelasticity theory. Results from the numerical simulation confirm the reciprocity principle and the superposition principle.     

A rigorous time domain analysis of gyrotrons

A self-consistent time domain analysis of gyrotrons is presented which allows studying multi-mode, multi-frequency operation. The electromagnetic field in the gyrotron cavity is expanded with respect to complete sets of eigenfunctions so that space charge effects are included in the analysis. Two improvements of the modal expansion inside gyrotron cavities are suggested which significantly increase the accuracy and the numerical efficiency of this method, namely, the removal of the non-uniform convergence of some field series at the coupling apertures and the estimation of the asymptotic values of some slowly converging series related to the modal analysis by a moderate number of cavity eigenfunctions. Discrete Fourier transform is used to obtain the time dependence of the electromagnetic field. The electron beam is described by a set of relativistic single particles. It is demonstrated that the strong numerical requirements of the suggested method can be overcome by using a vector computer. Two gyrotrons are investigated, namely, a low Q 35 GHz TE₀₁- and a 150 GHz TE₀₃-gyrotron. Both oscillation build-up and steady state operation are investigated including mode competition and window reflections. The simulations show that the assumption of a monofrequent steady state operation of gyrotrons, which is made by the commonly used frequency domain methods, is not always justified.     

The diffraction of light at ultrasonic waves in acoustic resonators

A theoretical treatment is given of the diffraction of light by hypersonic waves excited in solid prismatic samples. For a fixed frequency, a set of modes exists in such a resonator. The modes differ in the spatial distribution of the field, which corresponds to a set of partial waves propagating over an entire solid angle. The diffraction occurs only at the partial waves which satisfy the Bragg condition and the diffraction pattern has the form of a circle consisting of a large number of points. An expression is found for the angular separation of adjacent points which correspond to different modes. It is shown experimentally that for the scattered light field in the far zone the diffraction patterns are similar to Shaefer-Bergmann patterns. Explanations are given for the shape and fine structure of these patterns. The structure of the diffracted light beams in the near zone is also studied and the frequency intervals between the excitation of the various resonator modes are measured. The experimental results are in qualitative agreement with the theory.     

Stability analysis of nonlinear microwave circuits in time domain

Frequency-domain based methods are not valid to analyze a nonlinear microwave circuit with general, arbitrary nonlinearities. Therefore, analysis of nonlinear microwave circuits in time-domain is presented. Subharmonics and instabilities can be predicted. As examples, Josephson junction and the Schottkybarrier mixer diode are discussed.     

Propagation of short lightpulses in microring resonators: Ballistic transport versus interference in the frequency domain

The propagation of short lightpulses in waveguiding structures with optical feedback, in our case optical microresonators, has been studied theoretically and experimentally. It appears that, dependent on the measurement set-up, ballistic transport or interference in the time domain of fs and ps laser pulses can be observed. The experiments are analyzed in terms of characteristic time scales of the source, the waveguide device and the detector arrangement and are related to Heisenberg’s uncertainty principle. Based on this analysis, a criterion is given for the upper bit-rate for error free data transmission through optical microresonators.     

Advanced analysis concepts for terahertz time domain imaging

Imaging based on ultrashort terahertz (THz) pulses (100-3000 μm) is investigated. The measured pulses are analyzed and the resulting amplitude and time delay information are compared. An algorithm for discrimination of multiple pulses is presented, which can distinguish several layers inside an object. A new measurement concept is presented, which accelerates the measurement of samples with small optical path differences about two orders of magnitudes. Exemplarily different applications from the field of quality management are shown.     

Finite difference time domain analysis of a photonic crystal substrate patch antenna

Planar microstrip patch antennas can achieve a wide range of radiation patterns. However, due to surface-wave losses, they have low bandwidth, low gain, and a potential decrease in radiation efficiency. In order to minimize the surface-wave effects, a photonic-band gap (PBG) substrate is proposed. The PBG structure significantly diminishes the surface-wave modes and thus improves the gain and far-field radiation pattern and efficiency. In this paper, using FDTD, an accurate full-wave analysis of surface-wave propagation in a rectangular microstrip patch antenna with and without PBG is presented. Finally, the antenna fabricated and result of measurement was compared with numerical simulation.     

Nonlinear ultrasonic phase-conjugate beams and their application in ultrasonic imaging

The latest results of experimental and theoretical research into phase conjugation of nonlinear ultrasonic beams are generalized, and prospects for the development of nonlinear ultrasonic imaging are outlined.     

Cavitation in a periodontal pocket by an ultrasonic dental scaler: A numerical investigation

Periodontal pockets are spaces or holes surrounded by teeth under the gum line. These pockets can become filled with infection-causing bacteria resulting in tissue, bone, and tooth loss. Cavitation produced by the oscillating tip of dental ultrasonic scalers plays a significant role in routine periodontal therapy to clean these areas. Numerical studies were conducted for a scaler vibrating in a periodontal pocket which was simplified to a hole, using ABAQUS based on the finite element method. The simulations consider the three-dimensional, nonlinear, and transient interaction between the vibration and deformation of the scaler tip, the water flow around the scaler and the cavitation formation. The numerical model was validated by comparing results with experimental data for a scaler vibrating in an unbounded liquid, the displacement at the free end of the scaler and the cavitation pattern near the scaler tip displaying excellent agreement. A parametric study for a scaler vibrating in a hole has been carried out in terms of the volume of the hole, the taper ratio (the radius ratio between the circular opening and bottom of the hole), and the immersion depth of the scaler tip in the hole. The amount of cavitation generated is evaluated by the cavitation density (or the void fraction) which is the ratio of the volume of the cavitation occupied in the hole to the total volume of the hole. Numerical results indicate that the cavitation density in the hole increases with the decreasing hole volume and the increasing taper ratio. It is inferred that cleaning effects could be increased if some modifications to the scaler design could be made to increase the blocking effect of the hole during the cleaning process. Cavitation is observed in the hole even if the scaler is placed above the hole and increases with the immersion depth.     

基于FDTD的时域混合方法及其在天线前门耦合数值模拟中的应用

强电磁脉冲环境下的平台-机载天线一体化耦合计算属于典型多尺度时域电磁计算问题,采用传统的FDTD方法数值模拟时,由于精细结构的存在导致网格量巨大,计算效率低下。介绍了一种将非均匀FDTD方法与细导线FDTD方法以及多网格集总元件FDTD方法相结合的时域混合方法,能够有效降低计算开销,结合并行计算技术,快速计算得到天线端口上耦合产生的瞬态电压和电流响应,并将该方法成功应用于无人机平台-天线一体化前门耦合数值模拟中。